Method for simulation of an electric stimulation in an MR imaging system

ABSTRACT

A novel method is described for simulation of an electric stimulation of the nerve system subject to the rate of change of gradient fields. A gradient signal is filtered and a stimulation signal is derived, which is compared with a predetermined stimulation threshold value. An indicator signal is generated if the threshold value is exceeded. Therefore the time dependent and spatially dependent electric fields as defined by the scanning sequence and the gradient coil properties are calculated. A vector combination of said calculated electric field components from each gradient coil axis is performed, which results in a temporal diagram of the total electric field at various spatial locations within the gradient coil. The stimulation probability at each location from said temporal diagram and said stimulation signal is then calculated, and said stimulation probability is compared with the stimulation threshold value at each location within the gradient coil.

BACKGROUND

The following relates to methods, apparatuses, and computer programproducts related to simulation of an electric stimulation of the nervesystem in a magnetic resonance (MR) imaging system.

BRIEF SUMMARY

Modern MRI systems utilize high gradient amplitudes and slew rates. Whenthe rate of change (dB/dt) of the magnetic field gradients exceed aspecific threshold, the patient experiences peripheral nerve stimulation(PNS). PNS is an undesirable effect and the maximum rate of change ofthe magnetic field gradients used in an MRI system is regulated by theIEC and FDA. In specific examples it is generally possible to predictwhen PNS will occur by equating the rate of change of the magnetic fieldgradient to the electric field (E) that is generated inside the humanbody as a result of Maxwells equations. A simple model of the temporalresonse of the human nerve to this E-field yields a reasonableprediction of PNS when only simple waveforms are considered. Such simpleapproaches generally fail when any of the following conditions are met:

-   -   the gradient waveforms are discontinuous and not bipolar,    -   more than one gradient axis is used simultaneously,    -   the patient is placed at different positions with respect to the        gradient coil,    -   the gradient coil design varies from system to system.

It is general practise, on a clinical MRI system, to use the simple andconservative model to predict PNS. It is then often the case that thescan performance is limited unneccessarily due to the conservative(worst case) nature of the models used. In recent years, some effort hasbeen made to realize more accurate and flexible models.

Basically the following is known: At the nerve end, an electric field Eparallel to the nerve can cause an ion current through the nervemembrane (cf. J. P. Reilly, Electrical Stimulation andElectro-pathology, Cambridge University Press, 1992, pp. 213-217 and pp.27-280). In a region where the nerve is continuous, the ion current isdriven by the first derivative of E. The ionic charge that is built up,can become large enough to create an avalanche, corresponding to nerveexcitation. The avalanche propagates along the nerve to the next nodeetcetera. At long excitation duration, the estimated requiredintra-patient value of E is 6 V/m (at the nerve end). For shorterexcitations, the required field strength increases and thecharacteristic time involved is about 0.1-0.4 ms. Irnich points out thatthe situation is not equivalent to an RC circuit; instead, the relationbetween stimulus duration τ and threshold stimulus th is hyperbolic (cf.W. Irnich, F. Schmitt, Magnetostimulation in MRI, Mag. Res. Med., 33: p.619-623, 1995). The long duration limit value of stimulus is called therheobase rb and the characteristic time is called the chronaxie ch. Informula:

$\begin{matrix}{{{th}(\tau)} = {{rb}\left( {1 + \frac{ch}{\tau}} \right)}} & (1)\end{matrix}$

The Reilly threshold model and the comments of Irnich are based onexperimental work with single electrically induced stimuli. Such stimuliare quite different from the typical repeated stimulus generated by thegradient waveform in the MR system. Nevertheless, the Reilly thresholdmodel can be applied to interpret experimentally observed PNS in MRsystems. Early work of Budinger (T. F. Budinger et. al., Physiologicaleffects of fasi oscillating magnetic field gradients, JCAT 1991; 15, p.909-914), Mansfield (P. Mansfield, P. R. Harvey, Limits to NeuralStimulation in EPI, Mag. Res. Med. 1993; 29, p. 746-758) and Harvey (P.R. Harvey, P. Mansfield, Avoiding peripheral nerve stimulation: gradientwaveform criteria for optimum resolution in EPI, Mag. Res. Med. 1993,32, p. 236-241) illustrate the Reilly model.

It is further supposed in U.S. Pat. No. 6,169,403, on the basis of thedB/dt model (Irnich), that the stimulations caused by an externalelectric field and the relay (transmission) thereof in the nervoussystem are approximately described by the filtering of thedifferentiated gradient signal G_(diff)(t) with a first filteringfunction f_(F1)(t) and by filtering of its rectified portion Abs(G_(diff)(t)) with a second filtering function f_(F2)(t). The gradientsignals G(t) are measured by the electric current through the relatedgradient coil. The first filtering function f_(F1)(t) describes hereinthe excitation of the action potential on the presynaptic side, whichcauses chemical messenger substances to be diffused out, and isprocessed in a first low pass filter stage. These messenger substancesare absorbed on the postsynaptic side, i.e. in nerve cells downstream,where they trigger a further action potential. The excitation of theaction potential at the postsynaptic side is described by the filteringfunction f_(F2)(t). Since the original polarity of the excitation is nolonger contained in the action potential at the postsynaptic side, onlythe rectified portion of the differentiated gradient signal G_(diff)(t),which is designated Abs (G_(diff)(t), is processed in a second low passfilter stage. Thus, the aborting of the executed measuring sequenceoccurs given the crossing of a threshold value in an online monitoring.This crossing of the threshold value is signaled prior to the executionof the measuring sequence in a look-ahead monitoring.

To account for the discontinuous nature of the generally used waveforms,the concept of convolution of the gradient waveform with the temporalresponse of the nerve was introduced (cf. J. A. den Boer, Generalizationto complex shape of the nerve stimulation threshold based on existingknowledge of its relation to stimulus duration for rectangular. stimuli,ISMRM 1999, p. 108). In this model a simple representation of thetemporal response of the nerve is used which does not account accuratelyfor changes in response as a result of repeated waveforms. This modelexplains the waveform dependency of the PNS threshold, but not theobservation by Budinger (supra) and Hebrank (F. Hebrank, M. Gebhardt,SAFE model-a new method for predicting PNS in MRI. ISMRM 2000, p. 2007),who showed that the threshold for a single bipolar waveform graduallydecreases when the waveform is repeated more and more often. For aperiodic waveform with ramp times of 0.4 ms, the final threshold levelis reached after about 10 ms.

The present invention has the aim to provide a more accurate model ofthe stimulation of peripheral nerves in order to optimize the thresholdsettings in the MR system.

BRIEF DESCRIPTION OF THE DRAWINGS

Further advantages are disclosed in the following description in whichan exemplified embodiment of the invention is described with respect tothe accompanying drawings.

FIG. 1 a diagram of the spatio-temporal model for PNS predictionaccording to the present invention,

FIG. 2 a rectifying filter with weight dependent stimuli of oppositepolarity,

FIG. 3 another rectifying filter with weight dependent stimuli of singlepolarity,

FIG. 4 the combined filter according to the present invention,

FIG. 5 a diagram of the stimulation threshold versus gradient rise time,

FIG. 6 a diagram of the stimulation threshold as a function of thestimulation length, and

FIG. 7 a diagram of the stimulation threshold versus the number ofgradient signals,

FIG. 8 shows a print-out of the user screen of the console of an MRIapparatus,

FIG. 9 shows a gradient waveform plot,

FIG. 10 shows a PNS prediction plot as calculated,

FIG. 11 shows a screen print-out showing the sequence parameters,

FIG. 12 shows another gradient waveform plot,

FIG. 13 shows another PNS prediction plot,

FIG. 14 shows a balanced FFE with higher gradient amplitude,

FIG. 15 shows a further gradient waveform plot,

FIG. 16 shows a further PNS prediction plot, and

FIG. 17 shows a practical embodiment of an MR device for executing theabove-mentioned method for simulation of PNS.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

Specific numbers dedicated to elements defined with respect to aparticular figure will be used consistently in all figures if notmentioned otherwise.

Since a more general model for the temporal nature of the nerve behavioris established, the next challenge is to incorporate spatial informationof the time varying E-fields into the model. When the exact temporal andspatial nature of the time dependent gradient and E-fields generatedduring an MRI scan is taken in consideration, scan parameteroptimization, and system operation, closer to the limits of PNS can beenabled. This is the basis of the present invention.

According to the diagram in FIG. 1 a more accurate temporal model forthe peripheral nerve response to time varying magnetic (B) and electric(E) fields can be presented in a flow diagram of the sequences of eventsrequired to determine if PNS will occur with a particular scanningmethod. As such it describes the functionality of the software code thatis required to implement such a check on an MRI system. Firstly thespecific MR imaging method is chosen by the user and the parameters aredefined. In a preliminary approach prior to the beginning of magneticresonance imaging, the explicit knowledge of the magnetic design orproperties of the gradient coils GC1 and GC2 and the actual measuredparameters of the specific gradient coil as shown in box 1 areimplemented in decision step 2. Especially, the sequence parameters suchas slice angulation, number of slices, gradient coil signal etc. for aperiod of a single repeating cycle TR are provided in box 1. In nextstep 3 the differentiated gradient signal is filtered. Thereafter thetime dependent and spatially dependent E-fields for each gradient axis(G_(x), G_(y) and G_(z)) as defined by the scanning sequence and thegradient coil properties over a single cycle TR (either in vacuum or ina cylindrical body model) are calculated in step 4. Optionally in step5, a 3D mask based upon a preliminary or scout scan can be obtained, inorder to determine exactly where and how the patient is positionedinside the imaging volume. With such a spatial masking of the E-fieldspace the orientation and position of the body of the patient within thegradient coil can be identified and the number of calculations can bereduced. In following step 6 the vector sum of the E-field componentsfrom each gradient coil axis over a single cycle TR is calculated, whichresults in a time dependent description of the overall or net E-field atvarious spatial locations within the gradient coil. In step 7 the resultof the vector sum is extrapolated over N times the repetition time TRand the number M of slices. Therein the encoding steps and the sliceangulations are included. Optionally in step 8, additional informationcan be included, that relates to patient size and weight (which can bederived from the RF power calibration) in order to fine tune thethreshold settings of the stimulation model on a patient by patientbasis. In step 9 the so determined spatio-temporal E-field componentsare inputted into the stimulation prediction model:

$\begin{matrix}{\overset{\_}{E} = {{\frac{1}{\tau} \cdot {\int_{\tau}{{E(t)}\ {\mathbb{d}t}}}} \geq {E_{r} \cdot \left( {1 + \frac{\tau_{0}}{\tau}} \right)}}} & (2)\end{matrix}$wherein τ the stimulus duration and τ₀ the characteristic time orchronaxie (see FIG. 4).

The prediction or stimulation probability is evaluated for eachE_(x)(t), E_(y)(t) and E_(z)(t) independently. The nerve response iscalculated as a function of space and time to yield threespatio-temporal PNS stimulation probability trajectories. In step 10 thetime points are determined where the probability of PNS exceeds thethreshold at any point in the volume, for any of the E-field components.If in decision step 11 stimulation is not predicted then the scan can beexecuted—step 12, otherwise the sequence parameters will be modified instep 13 and the modified parameters are implemented in step 3 foranother iteration. The modifications concerns the slew rate of the wholescan, the swap of the gradient polarity, skipping acquisitions andputting gradients to zero at critical points, etc. Since the exact pointin time, of nerve stimulation, can be identified in advance, the optionexists to modify the sequence in its entirety, or just around the timepoint of stimulation, so as to prevent the occurrence of nervestimulation.

The proposed novel model of PNS extends the concept of convolution ofthe induced current, or E-field, waveform and the nerve response. Thefollowing properties of the nerve have been observed and documented:

-   -   The nerve responds in a non-linear way depending upon the        relative polarity, and timing, of successive stimuli.    -   Following activation of the nerve, there is a refractory period        (recovery time) during which the nerve can not be stimulated any        more.    -   Repeated stimulation leads to a de-sensitization of the nerve        (or at least the perception).

From the above mentioned observations it is concluded that the nerveresponse to a train of unipolar stimuli is different to a train ofbi-polar stimuli. It is known that a negative going stimulus can onlycancel the effect of a positive going stimulus under very specificconditions. In general, an equal amplitude negative stimulus, followinga positive stimulus, will not prevent nerve excitation. Therefore, it isconcluded that the sensitivity of the nerve to opposite polarity stimuliis modified by the effect of the previous stimuli (ionic concentrationis not reversed completely).

To model this behavior, a filter 20 is utilized which weightsdifferently stimuli of opposite polarity as is shown in FIG. 2. Thepartially rectifying filter 20 also accounts for the nerve recovery timemechanism which is also resulting from non-immediate reversal of ionicconcentration. Even partial, but incomplete, excitation can change thesensitivity of the nerve to the stimuli that will follow. The filter 20accounts for that mechanism. The output, following the filter,represents some measure of the potential for the nerve to be stimulated.When the input is the E-field, then the output represents the fractionof that E-field that can be compared with the required threshold forstimulation. When the ratio is equal to 1, then stimulation occurs.

The observation that repeated stimuli leads to a lower threshold can bemodeled by making the stimulation threshold dependent on the totallength of the stimuli. For a complex MR sequence this implies that thewhole waveform is taken across many repetition times TR. It is reasonedthat final stimulation ultimately depends upon the polarity of theinitial stimulus since the sensitivity to subsequent stimuli of oppositepolarity is reduced as described above.

The second filter 21 as shown in FIG. 3 operates over a longer timescale and considers only the stimuli of a single polarity. The output ofthis filter 21 behaves like a DC addition to the stimulus potential.This depends upon the longer time scale duration of the stimuluswaveform. There is also an element of bias towards the initial polarityof the stimulus. When the input is the E-field waveform, the outputrepresents a fraction of this E-field that must be added to the outputof the first filter 20, thereby making the possibility to reach thestimulation threshold more likely. The outputs from the two filters 20and 21 are therefore summed.

An additional measure is required because it is not known which polarityof E-field the nerve inside a human body is exposed to. This dependsupon many factors, not least the location of the nerve with respect tothe gradient coil. Since the model up to now is polarity sensitive, itis necessary to account for the fact that the initial polarity cannoteasily be known. This is done by simply calculating the inverse of theinput waveform before applying the two filters 20 and 21. The summedoutput is then compared with the output calculated using the originalwaveform. The final output is whichever is the maximum of both models asa function of time.

FIG. 4 illustrates the model in its entirety. As mentioned above, it ispreferable to normalize the final output of the model to a calibratedthreshold such that an output below 1.0 indicates no stimulation and anoutput above 1.0 indicates stimulation. The differentiated waveform g(t)of the gradient coil is split in two parts. In the upper filter stage 20a, the negative part of the waveform g(t) is scaled with a factor 0.8.In the lower filter stage 21 a only a single polarity is considered.Thereafter the output signals of both filters 20 a and 21 a aremultiplied with a weighting factor α₁ and α₂ in multipliers 22 and 23respectively, whereas α₁+α₂=1. In this case α₁=0.6 and α₂=0.4.Thereafter, the output signals are summed in adder 24. Since thisoperation would be sensitive to the polarity of the waveform, the sameoperation is repeated for the inverse waveform -g(t) in upper filterstage 20 b and in lower filter stage 21 b. The maximum of both modelsobtained in comparator stage 25 is used as output.

In short, the new model has following important properties:

-   1. Utilization of a more accurate temporal model for nerve response    to time varying B- or E-fields.-   2. Incorporation of explicit knowledge of the magnetic design of the    gradient coils used.-   3. Calculation of the time dependent and spatially dependent    E-fields as defined by the scanning sequence and the gradient coil    properties.-   4. Vector combination of the E-field components from each gradient    coil axis resulting in a time dependent description of the net E    field at various spatial locations within the gradient coil.-   5. Calculation of the stimulation probability at each location using    the refined temporal model for the nerve response.-   6. Utilizing knowledge derived from the effect of patient loading,    as determined by the QBC RF power calibration, as a means to    determine patient size for the purpose of weighting the stimulation    probability for small or large patients and/or different body    positions.-   7. Identifying the position and time point of likely stimulation and    providing a warning to the operator.-   8. Optional refinement of the MR pulse sequence as a result of    feedback from the predicted stimulation probability.-   9. Optional spatial masking of the E-field space using a mask    derived from a preview MR image of the body within the gradient coil    (to identify body position and reduce the number of calculations).-   10. Incorporation of an explicit numerical description of the    electrical properties of the human body to aid in accuracy of the    E-field determination.-   11. The possibility to utilize the model with more than one gradient    coil type in the same MR system.-   12. Integration of all the above points in a software program which    is resident on the computer of an MR system and executed as part of    the general execution of each imaging scan.    Experimental Evaluation of the Novel Model

FIG. 5 shows validation of the model according to the present inventionagainst published data by F. Hebrank and M. Gebhardt in ISMRM 2000, p.2007. The first plot shows the performance comparing stimulationthreshold dB/dt in T/sec versus gradient rise time C in μsec. The dashedline 28 is the output from the novel model as presented here. The solidline 29 is the measured Hebrank data. The second graph in FIG. 6 showsthe results of the stimulation threshold dB/dt in T/sec as a function ofthe stimulation length D in msec. The agreement of the calculated data(dashed line 30) with the measured data from Hebrank (solid line 31) iswithin 10%. Thus the here presented novel model is at least as accurateas the Hebrank model. However, the trend behavior is better with thenovel model.

FIG. 7 shows the published Hebrank data and the accuracy of the SAFEmodel for comparison with FIG. 6. The solid dots 32 present the data ofa clinical study and the solid line 33 presents the calculated graphaccording to the SAFE model. At the ordinate again the stimulationthreshold dB/dt and at the abscissa the number of trapezoidal pulses P.

FIG. 8 shows a print-out of the user screen of the console of an MRIapparatus in which the above mentioned novel model have been tested.FIG. 9 shows the gradient waveform plot and FIG. 10 the PNS predictionplot as calculated. The software developed for the novel model performsa real-time MR method optimisation/design for various sequences andhardware parameters. It utilizes the above mentioned convolution methodand the novel model of the nerve to predict if peripheral nervestimulation can occur using the sequence shown under the parameterlimitations given. At the moment this prediction is displayed, per axis,in the form of the nerve response to the gradient stimuli. Values below1.0 are below the threshold and values above 1.0 represent stimulation.The PNS prediction algorithm is “trained” on the Hebrank data and doestake into account the longer term effects relating to the number ofgradient cycles. The effective length of the gradient coil is in thiscase 0.45 m as for a typical whole body gradient coil. In this case asimple FFE sequence is shown with gradient amplitude and flew ratelimited to 22 mT/m and 105 T/m/s. All three axes are sub-threshold forthis single repetition time TR although continuing the prediction tolater TR's may show that stimulation will occur. This is implied in theEPI sequence below.

In FIG. 11 the screen print-out is showing the sequence parameters foridentical sequence parameters (FOV etc.) as in to the previous caseabove (FIG. 8) except a 32 echo EPI readout is used. In this case thePNS threshold is predicted to be exceeded for the readout (measurement)axis. In this case the software would predict a stimulation. This isconsistent with the knowledge that FFE is less likely to producestimulation than EPI. In FIG. 12 the gradient waveform plot is depictedand in FIG. 13 the PNS prediction plot.

A balanced FFE with higher gradient amplitude is another issue shown inFIG. 14 (screen print-out), FIG. 15 (gradient waveform plot) and FIG. 16(PNS prediction plot). Here the supra-threshold situation B to FFE andhigher gradient performance is investigated. In this example a gradientperformance of 40 mT/m and slew rate 200 T/m/s is assumed with a typicalwhole body gradient coil. Now, for the same image parameters as above,PNS is predicted due to both the preparation axis and the measurementaxis.

A practical embodiment of an MR device for executing the above mentionedmethod for simulation of PNS is shown in FIG. 17, which includes a firstmagnet system 42 for generating a steady magnetic field, and also meansfor generating additional magnetic fields having a gradient in the X, Y,Z directions, which means are known as gradient coils 43. The Zdirection of the co-ordinate system shown corresponds to the directionof the steady magnetic field in the magnet system 42 by convention,which only should be linear. The measuring co-ordinate system x, y, z tobe used can be chosen independently of the X, Y, Z system shown in FIG.17. The gradient coils 43 are fed by a power supply unit 44. An RFtransmitter coil 45 serves to generate RF magnetic fields and isconnected to an RF transmitter and modulator 46. A receiver coil is usedto receive the magnetic resonance signal generated by the RF field inthe object 47 to be examined, for example a human or animal body. Thiscoil 45 represents an array of multiple receiver antennae. Furthermore,the magnet system 42 encloses an examination space which is large enoughto accommodate a part of the body 47 to be examined. The RF coil 45 isarranged around or on the part of the body 47 to be examined in thisexamination space. The RF transmitter coil 45 is connected to a signalamplifier and demodulation unit 50 via a transmission/reception circuit49. The control unit 51 controls the RF transmitter and modulator 46 andthe power supply unit 44 so as to generate special pulse sequences whichcontain RF pulses and gradients. The control unit 51 also controlsdetection of the MR signal(s), whose phase and amplitude obtained fromthe demodulation unit 50 are applied to a processing unit 52. Thecontrol unit 51 and the respective receiver coils 43 and 45 are equippedwith control means to enable switching between their detection pathwayson a sub-repetition time basis (i.e. typically less than 10 ms). Thesemeans comprise inter alia a current/voltage stabilisation unit to ensurereliable phase behaviour of the antennae, and one or more switches andanalogue-to-digital converters in the signal path between coil andprocessing unit 52. The processing unit 52 processes the presentedsignal values so as to form an image by transformation. This image canbe visualized, for example by means of a monitor 53.

1. A method for simulation of an electric stimulation of a nerve systemof a subject to be examined generated by a rate of change of gradientfields generated by one or more gradient coils of a magnetic resonanceimaging system, wherein a gradient signal is filtered with a filteringfunction, a stimulation signal is derived from said filtered gradientsignal, and said stimulation signal is compared with a predeterminedstimulation threshold value for generating an indicator signal if saidthreshold value is exceeded, the method comprising: spatially masking aspace of the electric field by a mask derived from a preview MR image ofthe subject's body within the gradient coil, calculating time dependentand spatially dependent electric fields as defined by a scanningsequence and the gradient coil properties within the mask, vectorcombining said calculated electric field components from each gradientcoil axis resulting in a temporal diagram of the total electric field atvarious spatial locations within the gradient coil, calculating astimulation probability at each location from said temporal diagram andsaid stimulation signal, comparing said stimulation probability with astimulation threshold value at each location within the gradient coil;and providing a warning of likely stimulation based on the comparing. 2.A method as claimed in claim 1, wherein the gradient signal isdifferentiated, and the differentiated gradient signal is filtered in afirst stage with a first bipolar filter and is parallel filtered in afirst unipolar filter, the output signals of both first filters areweighted and the weighted output signals are added.
 3. A method asclaimed in claim 2, wherein the inverse of the differentiated gradientsignal is filtered in parallel in a second filter stage with a secondbipolar filter and a parallel second unipolar filter, the output signalsof both second filters are weighted and the weighted output signals areadded to a second stimulation signal, which is compared with thestimulation signal and the maximum of both stimulation signals is usedas output signal for comparing with said threshold value.
 4. A method asclaimed in claim 2, wherein said first bipolar filter weightsdifferently stimuli of opposite polarity.
 5. A method as claimed inclaim 1, wherein knowledge of the magnetic design of the gradient coilsis incorporated in the calculation.
 6. A method as claimed in claim 1,wherein knowledge derived from the effect of patient loading is weightedin the stimulation probability for the size and/or position of thepatient.
 7. A method as claimed in claim 1, wherein the scanningsequence is refined by feedback of the predicted stimulation probabilitysignal.
 8. A method as claimed in claim 1, wherein the time dependentcomponents of the electric field in x-, y- and z-direction areextrapolated over multiple repetition periods and multiple slices.
 9. Amethod as claimed in claim 8, wherein the time points and positions inthe volume of the gradient coil are calculated for each component of theelectric field independently and each of the predicted stimulationprobability is compared with the stimulation threshold value.
 10. Amagnetic resonance imaging apparatus for obtaining an MR image from aplurality of signals and for simulation of an electric stimulation of anerve system of a subject to be examined, which stimulation is generatedby a rate of change of gradient fields, the simulation includingfiltering a differentiated gradient signal with a filtering function,deriving a stimulation signal from said filtered gradient signal, andcomparing said stimulation signal with a predetermined stimulationthreshold value for generating an indicator signal if said thresholdvalue is exceeded, the apparatus comprising: a main field magnet;gradient coils; means for filtering the differentiated gradient signalwith a filtering function including a first filter stage with a firstbipolar filter for filtering the differentiated gradient signal and afirst unipolar filter for parallel filtering said differentiatedgradient signal and weighing means, in which both output signals areweighted, and adding means, in which the weighted output signals areadded; means for calculating and vector combining time dependent andspatially dependent electric field components from each gradient coilaxis based on gradient signals defined by a scanning sequence andfiltered by the filtering means and the gradient coil propertiesresulting in a temporal diagram of the total electric field at variousspatial locations within the gradient coils; means for calculating astimulation probability at each location from said temporal diagram andsaid stimulation signal; means for comparing said stimulationprobability with the stimulation threshold value at each location withinthe gradient coil and generating an indicator signal if said thresholdvalue is exceeded.
 11. A magnetic resonance imaging apparatus as claimedin claim 10, wherein the space of the electric field is spatially maskedby a mask derived from a preview MR image of the subject's body withinthe gradient coil.
 12. A magnetic resonance imaging apparatus as claimedin claim 11, wherein the filtering means futher comprises a secondparallel filter stage with a second bipolar filter for filtering theinverse differentiated gradient signal during approximately a singlerepetition time period, with a parallel second unipolar filter forparallel filtering said inverse differentiated gradient signal duringapproximately ten or more repetition time periods, and weighing means,in which both output signals are weighted, and adding means, in whichthe weighted output signals are added to form a second stimulationsignal, and means for comparing said stimulation signal with said secondstimulation signal and means for defining the maximum of the stimulationsignal and the second stimulation signal as output signal for comparingwith said stimulation threshold value.
 13. A magnetic resonance imagingapparatus as claimed in claim 10, wherein said first bipolar filterweights differently stimuli of opposite polarity.
 14. A computer programproduct stored on a computer usable medium for forming an image by amagnetic resonance method including a method for simulation of anelectric stimulation of a nerve system of a subject to be examinedgenerated by a rate of change of gradient fields of a gradient coil of amagnetic resonance imaging system, the computer program productcomprising a computer readable program storage medium storinginstructions executable by a computer to control the execution of aplurality of steps comprising: filtering a differentiated gradientsignal of said gradient coil with a filtering function, the filteringincluding filtering the differentiated gradient signal in a first stagewith a first bipolar filter, parallel filtering said differentiatedgradient signal in a first unipolar filter, and weighting the outputsignals of both first filters and adding the weighted output signals,deriving a stimulation signal from said filtered gradient signal,comparing said stimulation signal with a predetermined stimulationthreshold value for generating an indicator signal if said thresholdvalue is exceeded, calculation of time dependent and spatially dependentelectric fields as defined by a scanning sequence and the gradient coilproperties, vector combination of said calculated electric fieldcomponents from each gradient coil axis resulting in a temporal diagramof the total electric field at various spatial locations within thegradient coil, calculation of a stimulation probability at each locationfrom said temporal diagram and said stimulation signal, and comparingsaid stimulation probability with a stimulation threshold value at eachlocation within the gradient coil; and generating said indicator signalif said threshold value is exceeded at any location within the gradientcoil.
 15. A computer program as claimed in claim 14, wherein thefiltering further includes: filtering the inverse of the differentiatedgradient signal in a second filter stage with a second bipolar filterduring approximately a single repetition time period, parallel filteringsaid inverse signal with a parallel second unipolar filter duringapproximately ten or more repetition time periods, weighing both outputsignals, adding the weighted output signals to a second stimulationsignal, comparing said first stimulation signal with said secondstimulation signal and defining the maximum of both stimulation signalsas output signal for comparing with said stimulation threshold value;filtering the inverse differentiated gradient signal in parallel in asecond filter stage with a second bipolar filter filtering said inversesignal in a second the output signals of both second filters areweighted and the weighted output signals are added to a secondstimulation signal, which is compared with the first stimulation signaland the maximum of both stimulation signals is used as output signal forcomparing with said threshold value.
 16. A computer program as claimedin claim 14, wherein said first bipolar filter weights differentlystimuli of opposite polarity.